Search that does not explode: Six combinatorial walls, and an escape for each

A mind that learns small machines from 60 button presses meets the same limit in six places: recognising adevice, matching its parts, planning, merging memories in sleep, mapping a device built from parts, andgrowing its own methods. Done naively, each tries every option, and the options grow factorially orexponentially with the device or the memory. We tested an escape for each on standalone twins of themechanisms, pre-registering every claim and judging it once on fresh lifetimes. Placing the best-evidenceddisplay first and reasoning outward (anchoring) finds the exhaustive answer on 479 of 480 devices, at 2.12.7× more cost per size step where trying every renaming costs about 11× more. Being reminded byfamiliarity and situation, stopping on a held-back fit, and holding a guess that is familiar but not yet placedrecognises 96% of devices in a 483-drawer memory with 30 alignments; checking every drawer takes 483for the same 96%. An exact planner that skips branches which cannot win reaches the same goals astrying every sequence with 0.5–1% of the work. It also exposes a bias in the current cap, which drops fargoals to 6–7% where 1,024 sequences drawn at random, the cheapest fix, reach 90–92%. Sleep lumpslookalike memories because it judges kinship on too few devices. A test that holds the amount of datafixed keeps them apart 97.5% of the time with 26% of the reads of checking every device, where a randomsample of 16 devices, the floor, keeps them apart 96%. A map built from parts and learned wiring predicts a729-state device at 0.95 nats per press, where a flat map scores 6.55 and knowing nothing scores 6.59.Carrying winning runs of pieces across lifetimes lifts the share of growth lines that find a planner from10.5% to 50%. Of 49 pre-registered claims, 18 failed, and each is reported. We then checked three escapesin the LOCUS engine on development lifetimes. The exact planner returned the same best plan as tryingevery sequence on all 4,076 recorded planning moments. Anchoring returned the exhaustive answer on98.7% of 91,112 recorded comparisons, short of the identical answers the engine requires. The sizematched sleep test predicted worse than reading every device on 12 of 12 lifetimes; its floor, a randomsample of 16 devices per drawer, predicted better on 13 of 16 and kept sleep’s cost per device flat over1,500-device lifetimes.